Pythagorean Theorem

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Pythagorean Theorem

• By Matt Enderle

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Overview

• Pythagoras and a brief history of mathematics
• Pythagorean Triples
• Proof of the Pythagorean Theorem
• Examples and fun stuff

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Pythagoras

• Who was he?
• Greek philosopher (560 BC- 480 BC), and religious
  leader who had done quite a bit for mathematics,
  astronomy, and music
• Developed the Pythagorean Theorem

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Pythagorean Triples

• These are numbers which will make up any right
  angle such as 345 where 3 and 4 are two legs of
  the triangle and 5 is the hypotenuse

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Formula for a Triple

• Suppose m and n are two positive integers, with
  mltn.
• Then n²-m², 2mn, and n² m² should all equal a
  Pythagorean Triple.
• Ex. 1) m1 n2
• Ex. 2) m3 n4

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Pythagorean Theorem

• Defined as- The theorem that the sum of all the
  squares of the lengths of the sides of a right
  triangle equal to the square of the length of the
  hypotenuse.
• Mathematically- c² a² b²

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Prove it!

• Ex. 3) Leg 13, Leg 24, Hyp. 5
• Ex. 4) Leg 115, Leg 212, Hyp.13

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EXAMPLE TIME!!!